Implementation and Evaluation of Ate Pairings on Elliptic Curves with Embedding Degree 10 Applied Type-II All-One Polynomial Extension Field of Degree 5

Pairing-based cryptography has received much attention as an encryption method for realizing advanced cryptography such as ID-based encryption and searchable encryption. In a pairing-friendly elliptic curve of embedding degree 10, calculation cost of multiplication and squaring on extension fields of degree 5 are related to efficiency of pairing. Therefore, it is necessary to select an efficient multiplication and squaring algorithms on the extension field of degree 5. To apply these algorithms, the authors implement a pairing on an elliptic curve of embedding degree 10 with type-II all-one polynomial extension field (AOPF) of degree of 5 and optimal extension field (OEF) of degree of 5. As a result, the computational complexity of pairing with the expanded AOPF of degree 5 are almost 7.4% efficient than that of the expanded OEF of degree 5.